Bridge Safety Analysis Based on the Function of Exceptional Vehicle Transit Speed

Roberto Ventura1, Benedetto Barabino1, *, David Vetturi2, Giulio Maternini1
1 Department of Civil, Environment, Land and Architecture Engineering and Mathematics (DICATAM), University of Brescia, Brescia, Italy
2 Department of Mechanical and Industrial Engineering (DIMI), University of Brescia, Brescia, Italy

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© 2020 Ventura et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at Department of Civil, Environment, Land and Architecture Engineering and Mathematics (DICATAM), University of Brescia, Italy; E-mail:



The road management agencies often prescribe very low-speed limits for exceptional vehicles transiting on the deck. These restrictions aim to reduce the dynamic effects due to the vehicle-bridge interaction because it is assumed that these effects increase with speed. However, sometimes, a reduction in speed increases the encounter probability of two exceptional vehicles travelling in opposite directions and this could compromise the safety of the bridge when the total masses of both vehicles exceed the bridge bearing capacity (or limit mass).


While the literature has investigated the encounter probability in a theoretical way and has investigated the vehicle-bridge interaction, especially in terms of dynamic load increment, to the best of our knowledge, no study has investigated the conjunction probability of encounters and of exceeding the limit mass also by using real data. This paper aims to cover this gap by proposing an integrated model that computes the “Annual Probability of Failure” of the bridge, defined as the likelihood to exceed the “Limit Mass" of the deck when two opposite exceptional vehicles encounter.


According to the probability theory, the “Annual Probability of Failure” can be obtained by multiplying the likelihood that during the reference year, at least once, two exceptional vehicles, travelling in two opposite directions (ascendant and descendant), will be simultaneously on the bridge deck (“Annual probability of encounter”) with the likelihood that the sum of the single masses of two exceptional vehicles randomly extracted from the sample, including the dynamic effects, exceeds the limit mass ml (“Probability of exceeding the limit mass”).


The results show that the probability of encounter increases with both the exceptional vehicles flow rate and the length of the span, whereas it decreases with the passing speed. The probability of exceeding the limit mass increases with speed. Nevertheless, by combining both the probabilities, these results suggest the existence of an “Optimal Speed”, which minimizes the “Annual Probability of Failure”.


The existence of an “Optimal Speed” should be considered when defining the exceptional vehicle transit rules on bridges as well as the speed limit.

Keywords: Bridges, Exceptional vehicles, Optimal speed, Probability of failure, Probability of encounter, Safety, Limit mass.